Present value formulas

Symbols: FV future value, PV present value, n periods, r interest rate per period (as a decimal, e.g. 6% → 0.06), PMT payment per period.

One future payment (lump sum)

Discount a single amount due in n periods:

PV = FV ÷ (1 + r)ⁿ

If n = 0, PV = FV. If r = 0 and n > 0, PV = FV as well (no discounting).

Level payments (annuity)

Ordinary annuity (payment at the end of each period), r ≠ 0:

PV = PMT × (1 − (1 + r)⁻ⁿ) ÷ r

If r = 0, PV = PMT × n.

Annuity due (payment at the beginning of each period): multiply the ordinary-annuity PV by (1 + r).

These match the logic behind the periodical deposits calculator on the home page.